Most of those games make the use of the teleport obligatory, with level design all made towards its use. We didn't want to do it like that, but to have the teleport as an extra feature you can use to beat the game. But like the shield in Gigawing, you can finish the game without ever using the teleport if you want to give it a try.
A few patterns will be a lot easier if you use the teleport... but the game was fully designed so you could finish it by just dodging bullets normally and shooting , at least the arcade mode

The Cadet School mode does have a few levels where using the teleport is obligatory, but then those are very short levels and each one has a very different feeling from the previous one.
Also, some of the telports have some extra resources. Nina's teleport, for example, leaves a drone ship at the original point... most of the enemy fire then will be aimed at the drone (which also keeps firing from the original point - and also can pickup the bonus icons), so you can use it to, for example, focus firepower at one point of the screen while you move to another point to grab bonus icons. Or you can use it to just draw enemy fire to another point of the screen.
Leo's teleport leaves a black hole on the original point, which sucks into it basically everything... enemies, enemy bullets, bonus icons, your own bullets... you can use it to escape but also to make one area of the screen really safe if you want it to.
Z2's teleport is actually extremely offensive, you dash into a direction doing heavy damage to all enemies on its way . It's the teleport with the quickest cooldown time (1.5 seconds IIRC), so you can use it a lot to just keep killing enemies and collecting the bonus at full value.
And so on and on and on

There are 9 different ships to choose from, and each one will lead to a very specific playstyle. At least that's what we tried to do.
I uploaded a small gameplay video taken from the demo. Quality isn't very good and it's only in 30 fps (game runs at 60fps obviously), but it gives an idea of what the demo is about.
https://www.youtube.com/watch?v=lel4lX3kLmY